Analysis of π-mode Stopband in an Asymmetric Millimeter-Wave Helical Slow-Wave Structure

Abstract

A simple closed form formula for the estimation of π-mode stopband in an azimuthally asymmetric helical slow-wave structure (SWS) was developed following coupled-mode analysis of multiple reflections of the degenerate space-harmonic modes from the support rod discontinuities. The method incorporates the effects of circuit loss, and accrues the accuracy of 3D electromagnetic analysis by allowing the use of dispersion characteristics obtainable from any standard electromagnetic modeling. The formula is simple and amenable to easy computation, even using a scientific calculator, and without resorting to exhaustive and time-intensive numerical computation, and at the same time, without sacrificing the accuracy in results. The analysis was benchmarked against published results and excellent agreement observed. The analysis was further used for demonstrating the stopband phenomenon for a typical millimeter-wave helical slow-wave structure. Compared to low frequency structures, the stopband phenomenon for a millimeter-wave structure was found to be more pronounced, and an interesting inference was drawn as to how asymmetry induced stopband might be made to advantage in combating π-mode instabilities in a millimeter-wave traveling-wave tube.